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Definition df-bdop 29611
Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 29499 for definition of operator.) (Contributed by NM, 18-Jan-2006.) (New usage is discouraged.)
Assertion
Ref Expression
df-bdop BndLinOp = {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}

Detailed syntax breakdown of Definition df-bdop
StepHypRef Expression
1 cbo 28717 . 2 class BndLinOp
2 vt . . . . . 6 setvar 𝑡
32cv 1529 . . . . 5 class 𝑡
4 cnop 28714 . . . . 5 class normop
53, 4cfv 6348 . . . 4 class (normop𝑡)
6 cpnf 10664 . . . 4 class +∞
7 clt 10667 . . . 4 class <
85, 6, 7wbr 5057 . . 3 wff (normop𝑡) < +∞
9 clo 28716 . . 3 class LinOp
108, 2, 9crab 3140 . 2 class {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
111, 10wceq 1530 1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop𝑡) < +∞}
Colors of variables: wff setvar class
This definition is referenced by:  elbdop  29629  hhbloi  29671
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